Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20276044 | C2 | semidirect |
| 3. #20275856 | C2 | semidirect |
| 5. #20272539 | C2 | semidirect |
| 7. C53×#1272 | C2 | semidirect |
| 196. #1272 | D53 | semidirect |
| 226. C53 | #7779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282697 | 2 |
| #20276044 | 2 |
| #20275856 | 2 |
| #20275800 | 2 |
| #20272539 | 2 |
| #20272535 | 2 |
| C53×#1272 | 2 |
| #7779 | 53 |